Surrogate models for plasma displacement and current in 3-D perturbed magnetohydrodynamic equilibria in tokamaks

• Published in: Nuclear fusion
• Main Authors: Liu, Yueqiang, Akcay, Cihan, Lao, Lang L., Sun, Xuan
• Format: Journal Article
• Language: English
• Published: IAEA IOP Publishing 25.10.2022
• ISSN: 0029-5515; 1741-4326

Abstract A numerical database of over one thousand perturbed three-dimensional (3-D) equilibria has been generated, constructed based on the MARS-F (Liu Y.Q. et al 2000 Phys. Plasmas 7, 3681) computed plasma response to the externally applied 3-D field sources in multiple tokamak devices. Perturbed 3-D equilibria with the n=1-4 (n is the toroidal mode number) toroidal periodicity are computed. Surrogate models are created for the computed perturbed 3-D equilibrium utilizing model order reduction (MOR) techniques. In particular, retaining the first few eigenstates from the singular value decomposition (SVD) of the data is found to produce reasonably accurate MOR-representations for the key perturbed quantities, such as the perturbed parallel plasma current density and the plasma radial displacement. SVD also helps to reveal the core versus edge plasma response to the applied 3-D field. For the database covering the conventional aspect ratio devices, about 95% of data can be represented by the truncated SVD-series with inclusion of only the first 5 eigenstates, achieving a relative error below 20%. The MOR-data is further utilized to train neural networks (NNs) to enable fast reconstruction of perturbed 3-D equilibria, based on the 2-D equilibrium input and the 3-D source field. The best NN-training is achieved for the MOR-data obtained with a global SVD approach, where the full set of samples used for the NN training and testing are stretched and form a large matrix which is then subject to SVD. The fully connected multi-layer perceptron, with one or two hidden layers, can be trained to predict the MOR-data with less than 10% relative error. As a key insight, a better strategy is to train separate NNs for the plasma response fields with different toroidal mode numbers. It is also better to apply MOR and to subsequently train NNs separately for the conventional and low aspect ratio devices, due to enhanced toroidal coupling of Fourier spectra in the plasma response in the latter case.